An Arizona family who set sail for the island nation of Kiribati to escape abortion, homosexuality and "the state-controlled church" in the US are back home after their boat foundered in the Pacific.

Hannah Gastonguay, 26, said she and her husband, Sean, 30, had "decided to take a leap of faith and see where God led us" when they took their two small children and her father-in-law and set sail from San Diego in May.

But after storms damaged the boat and left them drifting for weeks they had to be rescued by a Venezuelan fishing vessel, and were then transferred to a Japanese cargo ship and taken to Chile.

Sean Gastonguay told KTVK-TV he would now have to find work to repay the $10,000 the family borrowed from the US State Department to fly home.

The family moved from Arizona to San Diego last year and decided to head for Kiribati because they believed it was less likely to interfere with their religion.

"They say it's the least developed island so I figured: undeveloped, less corruption," Sean Gastonguay said.

US "churches aren't their own", Hannah Gastonguay said, suggesting that government regulation interfered with religious independence. "Jesus isn't the head of the church. God isn't the head of the church."

Among other differences, she said, they had a problem with being "forced to pay these taxes that pay for abortions we don't agree with".

Hannah gave birth to the couple's eight-month-old daughter Rabah on the boat before they left San Diego. Also on board were three-year-old Ardith and Sean's father, Mike.

At first the seas were calm, but later they were hit by storms. After they had been on the ocean for about two months they were down to "some juice and some honey" and what fish they could catch.

Still, we "didn't feel like we were going to die or anything," Hannah said. "We believed God would see us through."

At one point a fishing boat came into contact with them but left without providing assistance. A Canadian cargo ship came along and offered supplies, but when they pulled up alongside it, the vessels bumped and the smaller ship sustained even more damage.

They were getting hit by "squall after squall, after squall."

"The deck started separating from the hull, that was toward the end of it, the water would come in so we were constantly pumping and lots of stuff was getting damaged," Sean told KTVK.

"We were in the thick of it, but we prayed," Hannah said. "Being out on that boat, I just knew I was going to see some miracles."

Eventually, their boat was spotted by a helicopter that had taken off from a nearby Venezuelan fishing vessel, which ended up saving them.

"The captain said, 'Do you know where you're at? You're in the middle of nowhere,'" she said.

They were on the Venezuelan ship for about five days before transferring to the Japanese cargo ship, where they spent nearly three weeks before landing in the Chilean port of San Antonio.

Sean Gastonguay said he believed his family was never in real danger and had been blessed with meeting many new friends.

Hannah said now the family were back in Arizona they would "come up with a new plan".

• This article was amended on 16 August 2013. An earlier version said that the Gastonguay family had set sail for the tiny island of Kiribati. Kiribati is an island nation in the central Pacific Ocean, which consists of 33 coral islands divided among three island groups: the Gilbert Islands, the Phoenix Islands, and the Line Islands. There is no single island called Kiribati, but there is one in the Line group called Kiritimati.